Overloading a method in subclass (Enum vs int)

Why the following two code samples produce different output?

Case 1

enum EnumType
{
    First,
    Second,
    Third
}

class ClassB
{
    public string Func(int index)
    {
        return "Func(int)";
    }

    public string Func(EnumType type)
    {
        return "Func(EnumType)";
    }
}

class Program
{
    static void Main(string[] args)
    {
        ClassB b = new ClassB();
        Console.WriteLine(b.Func(0));
        Console.WriteLine(b.Func(EnumType.First));
        Console.ReadLine();
    }
}

Output:

Func(int)
Func(EnumType)

Case 2

enum EnumType
{
    First,
    Second,
    Third
}

class ClassA
{
    public string Func(int index)
    {
        return "Func(int)";
    }
}

class ClassB : ClassA
{
    public string Func(EnumType enumType)
    {
        return "Func(EnumType)";
    }
}

class Program
{
    static void Main(string[] args)
    {
        ClassB b = new ClassB();
        Console.WriteLine(b.Func(0));
        Console.WriteLine(b.Func(EnumType.First));
        Console.ReadLine();
    }
}

Output:

Func(EnumType)
Func(EnumType)

I am puzzled. Does it mean that Func(EnumType) hides Func(int) declared in the base? If this is the case then why literal 0 is implicitly casted to EnumType in the second case without a warning?

EDIT:

There is even more interesting behavior when I try

Console.WriteLine(b.Func(0));         
Console.WriteLine(b.Func(1));
Console.WriteLine(b.Func(EnumType.First));

What is your guess the output should look like?

here it is:

 Func(EnumType)
 Func(int)
 Func(EnumType)

Any ideas why 0 and 1 are treated differently?

EDIT 2:

It turns out that literal 0 indeed has special meaning in C#.

Here and here I found an excellent description of this behavior (see the accepted answers).